Power electronic circuits are used to control and condition electric power. For instance, power electronic circuits may be used to convert a direct current into an alternating current, to change voltage or current magnitude, or to change the frequency of an alternating current.
An inverter is a power electronic circuit which receives a dc source signal and converts it into an ac output signal. Harmonic neutralization and pulse-width modulation techniques are used to generate the ac signal. Harmonic neutralization involves a combination of several phase-shifted square-wave inverters, each switching at the fundamental frequency. Pulse-width modulation involves switching a single inverter at a frequency several times higher than the fundamental.
Inverter switching action generates transients and spurious frequencies in a power signal, usually in the form of harmonics of the switching frequency. The switching action may also produce electromagnetic interference (EMI) which is radiated or conducted through the supply line. While the internal design of an inverter is chosen to minimize transients and spurious frequencies, it is usually necessary to filter the input or the output of the inverter.
A growing number of nonlinear loads in the electric utility power network has resulted in increasing waveform distortion of both voltages and currents in ac power distribution systems. Typical nonlinear loads are computer controlled data processing equipment, numerical controlled machines, variable speed motor drives, robotics, medical and communication equipment.
Nonlinear loads draw square wave or pulse-like currents instead of purely sinusoidal currents drawn by conventional linear loads. As a result, nonlinear current flows through the predominantly inductive source impedance of the electric supply network. Consequently, a non-linear load causes load current harmonics and reactive power to flow back into the power source. This results in unacceptable voltage harmonics and supply load interaction in the electric power distribution in spite of the existence of voltage regulators.
The degree of current or voltage distortion can be expressed in terms of the relative magnitudes of harmonics in the waveforms. Total Harmonic Distortion (THD) is one of the accepted standards for measuring voltage or current quality in the electric power industry.
Apart from voltage and current distortion, another related problem may arise when nonlinear loads are connected to the electric power network. In particular, when the load current contains large amounts of third or other triplen harmonics, the harmonic current tends to flow in the neutral conductor of the power system. Under these conditions, the neutral current can exceed the rated current of the neutral conductor. Since the neutral is normally designed to carry only a fraction of the line current, overheating or even electric fires can result.
The generation of harmonic waveforms, fundamental frequency reactive currents, loads that cause sags and surges in the supply voltage, and unbalanced three phase currents has resulted in the emergence of standards such as IEC 555 and IEEE 519 which force greater attention on the converter-utility interface. The maximum allowable voltage THD and the individual harmonic voltages are specified by IEEE 519 harmonic standards for different voltage levels. By way of example, under the IEEE 519 standard, a 460V coupling must operate within the following harmonic injection parameters: 5th and 7th harmonics--7%, 11th and 13th harmonics--3.5%, 17th and 19th harmonics--2.5%, 23 and 25 harmonics--1%. Thus, for the 11th and 13th harmonics, no greater than a 3.5% THD may be injected back into the supply. Several utilities are now requiring that their industrial customers conform to the IEEE 519 standard.
A number of techniques have been utilized to reach these low THD values. Passive filters, such as LC tuned filters, are often used because they are efficient and inexpensive. On the other hand, there are a number of problems associated with passive filters. First, the source impedance strongly influences the compensation characteristics of the passive filter. Next, the passive filter may cause a parallel resonance with the ac supply, thereby causing amplification of the harmonic currents on the source side at specified frequencies. The passive filter may also cause a series resonance with the source, thereby causing significant voltage harmonics on the ac source. Another problem is that it is difficult to ensure that the background distortion on the utility supply does not overload the filter. Passive filters also tend to be susceptible to load and line switching transients. Finally, passive filters are sensitive to ac system impedances that change as a result of system configurations such as line switching; they are also sensitive to component tolerances. Since passive filters are designed for a specific load, they cannot be tuned to 5th, 7th, and other dominant harmonics of the load because they might be overloaded with supply side harmonics at the tuned frequencies. Hence, they have to be inherently off-tuned (for example, at 4.7 instead of 5). In such a case, the passive tuned filters are unable to absorb the dominant load harmonics. As a result, the dominant load harmonics will flow into the supply.
Active power filters have been used to resolve some of the problems associated with passive filters. Active power filters, or active power line conditioners (APLCs), inject signals into an ac system to cancel harmonics. Specifically, the injected signal has the same amplitude and reverse phase of the load current harmonics to be eliminated.
Active filters comprise one or two pulse width modulated inverters in a series, parallel, or series-parallel configuration. The inverters have a dc link, which can be a dc inductor (current link) or a dc capacitor (voltage link). It is advantageous to keep the energy stored in the dc link (capacitor voltage or inductor current) at an essentially constant value. The voltage on the dc link capacitor can be regulated by injecting a small amount of real current into the dc link. The injected current covers the switching and conduction losses inside the APLC. The link voltage control can be performed by the parallel inverter.
There are a number of problems associated with active filters. First, it is difficult to realize an active filter with large VA rating, rapid current response and low losses. Next, the initial and running costs are high compared to passive filters. Finally, the harmonic currents injected from the active filter may flow into other passive filters and capacitors connected on the ac system.
The use of hybrid passive-active filters has been proposed as a means for combining the lower cost of passive filters with the control capability offered by a small rating series active filter. In such a system, the passive filter absorbs all harmonic currents generated by the load, while the small series active filter provides harmonic isolation between the load and the power source (utility company). The series active filter is controlled to force all load harmonics into the passive filter, thereby achieving harmonic isolation between the load and the supply. This forces purely sinusoidal current in the ac line. All harmonic currents, are in principle, diverted to the passive filter which provides a low impedance path for the dominant harmonics.
A combined system with a shunt passive filter and a small rated series active filter is illustrated in FIG. 1. The system 20 includes a shunt passive LC filter 22 with a 5th tuned LC filter 24, a 7th tuned LC filter 26, and a high pass filter 28 connected in parallel with the load 30. A small rated series active filter may be realized with a three-phase inverter 34, such as a resonant dc link voltage source inverter. The inverter 34 uses six Insulated Gate Bipolar Transistors 36 with six feedback diodes 38. Naturally, other switching devices with intrinsic turn-off capabilities may be used. A dc capacitor 40 is used as a dc link voltage source. Transformers 42 are used to realize a serial coupling to the three-phase power lines 44A, 44B, and 44C which are energized by power supply 46.
Assuming that the series active filter realized by the voltage source inverter has large bandwidth and therefore behaves as an ideal controllable voltage source, a single phase equivalent circuit for the system of FIG. 1 is shown in FIG. 2(a). In FIG. 2(a), Z.sub.f is the impedance of the shunt passive filter system 22 and Z.sub.s is the source impedance. The harmonic producing load 30 acts like a current source. The control strategy is to modulate the series active filter 34 so as to ideally present a zero impedance at the fundamental frequency and infinite pure resistance at all the load current harmonic frequencies. In such a case, the load current harmonics are constrained to flow in the shunt passive filter, and the worst case harmonic voltage across the series active filter 34 is given by the arithmetic sum of the supply voltage harmonics, if present, and the shunt passive filter terminal voltage harmonics. The series active filter 34 is controlled to act as an active impedance, which differs from the conventional series or shunt active filters that are respectively controlled to act as a voltage source (zero impedance) or current source (infinite impedance).
FIGS. 2(b) and 2(c) show the equivalent circuit of FIG. 2(a) for the fundamental and the harmonics respectively, assuming zero impedance at the fundamental and a finite maximum resistance K (ohms) at all the harmonic frequencies of the load. It can be seen from FIG. 2(b) that no fundamental frequency voltage is applied to the inverter, and the shunt passive filter only acts as a power factor improvement capacitor of the load for the fundamental.
From FIG. 2(c), one may derive the following equations: ##EQU1##
Equations 1-3 indicate that if the series active filter 34 can be controlled such that K&gt;&gt;Z.sub.f, then the load current harmonics are constrained to flow into the shunt passive filter, instead of flowing back into the source. From FIG. 2(c), it can be seen that if the series active filter can be controlled such that the resistance K is much larger than the source impedance, Z.sub.s, then the source impedance will have no effect on the compensation characteristics of the shunt passive filter 22. Also, no ambient harmonics generated elsewhere in the system can flow into the shunt passive filter and hence the possibility of resonance condition between the source 46 and the shunt passive filter 22 is eliminated. Similarly, since no load current harmonics can flow into the source 46 or to other passive filters elsewhere in the system, the possibility of resonance condition between the load 30 and the source 46 (beyond the point of common coupling) is also eliminated. The series active filter 34 acts like a damping resistance to harmonics, which solves the problems associated with using only a shunt passive filter, such as anti-resonance and harmonic sinks to the power system. The series active filter 34 acts as a current controlled voltage harmonic source and does not inject any fundamental voltage. Hence, it does not effect the fundamental supply current which is dictated by the load and the passive filter system.
The equations also indicate that if the series active filter 34 can be controlled such that K&gt;&gt;Z.sub.f and K&gt;&gt;F.sub.v, then the harmonic voltages of the source V.sub.sh, applies only to the series active filter 34 and not to the shunt passive filter 22 terminal voltage Vf. In this case, harmonic voltages applied to the series active filter 34 are given by the vector sum of harmonic voltages generated by the load current harmonics flowing into the shunt passive filter, Z.sub.f I.sub.Lh, and the harmonic voltages of the source V.sub.sh. This is characterized by the following equation: EQU V.sub.ch =-Z.sub.f I.sub.Lh +V.sub.sh ( 4)
The first term on the right hand side of equation (4) relates to the harmonic impedance of the shunt passive filter and depends on the quality factor Q, of the shunt passive filter. The larger the value of Q, the smaller is the required VA rating of the series active filter. The second term on the right hand side of the equation depends on the harmonic voltage of the supply, V.sub.sh, which does not appear at the shunt passive filter terminal but is applied across the series active filter. In such a case the series active filter isolates the load current harmonics from the power system and the power system's harmonics from the load, and the series active filter acts as a "harmonic isolator". Due to the "harmonic isolator" action of the series active filter 34, the shunt passive filter 22 can be designed independent of the source impedance.
If the series active filter can achieve a value of K sufficiently larger than the source impedance, Z.sub.s, and the shunt passive filter impedance, Z.sub.f, for all load current harmonics, then the series active filter can achieve good harmonic isolation between the source and the load. The features and performance of the combined system of series active filter 34 and shunt passive filter 22 are greatly influenced by the filtering algorithm employed for the extraction of source current harmonics and the control scheme for the series active filter 34.
A synchronous reference frame regulator may be used to implement the described control strategy for the series active filter 34. The operation of the series active filter 34 is governed by a pulse-width modulator or a discrete pulse modulator which toggles the gates of the IGBTs 36 (or other active devices used in the filter) in a predetermined fashion.
Synchronous reference frame regulators have been widely used for controlling ac machines. In general, ac machine control theory is directed toward providing accurate mechanisms for controlling the torque of a machine. Torque control in an ac machine is obtained by managing a current vector composing amplitude and phase terms. The control of ac machines is complicated by the requirement of external control of the field flux and armature mmf spatial orientation. In the absence of such a control mechanism, the space angles between the various fields in an ac machine vary with load and result in oscillations or other unfavorable physical phenomenon. Control systems for ac machines which directly control the field flux and armature mmf spatial orientation are commonly referred to as "field orientation" or "angle" controllers. Such controllers employ synchronous transformations, as will be described below.
The fundamental principles of field orientation control of ac motors is described in Introduction to Field Orientation and High Performance AC Drives, IEEE Industrial Drives Committee of the IEEE Industry Applications Society, Oct. 6-7, 1986. Field orientation principles rely upon the fact that the rotor of a motor has two axes of magnetic symmetry. One axis is known as the direct axis, and the other axis is known as the quadrature axis. These terms are usually shortened to simply refer to the d-axis and the q-axis.
Field orientation techniques endeavor to control the phase of the stator current to maintain the same orientation of the stator mmf vector relative to the field winding in the d-axis within the d-q scheme. FIG. 3 depicts a symbolic representation of a field orientation control system and its corresponding mathematical model. The three phase system (a, b, c) is first synchronously transformed to a two phase ds-qs scheme which is stationary with respect to the three phase system. This 3-phase to 2-phase transformation is equivalent to a set of linear equations with constant coefficients, as shown in FIG. 3.
The second step is the synchronous transformation from stationary d-q variables to rotating d-q variables. This transformation involves the angle .THETA. between the two systems and is described by the matrices given in the figure. The rotation transformation is often referred to as a "vector rotation" since the d-q quantities can be combined as a vector and the transformation then amounts to the rotation of one vector with respect to the other. FIG. 3 includes the vector rotation equations.
FIG. 4 depicts the inverse synchronous transformations to those performed in FIG. 3. Initially, a rotating-to-stationary synchronous transformation is made using the matrices depicted in FIG. 4. After the stationary rotor reference frame variables are established, a two phase to three phase synchronous transformation is made, consistent with the equations provided in the figure.
FIG. 5 shows a control scheme specifically directed to the series active filter of FIG. 1. The three-phase source currents, i.sub.sa, i.sub.sb, i.sub.sc are measured and transformed from three-phase to two-phase stationary reference frame ds-qs quantities using a 3 -to-2 phase transformer 50A. The 3-to-2 phase transformer executes the following equation: ##EQU2##
The stationary reference frame ds-qs source currents from the 3-to-2 phase transformer 50A are then transformed to a synchronous rotating de-qe reference frame by a stationary-to-rotating transformer 52A which executes the following equation: ##EQU3##
The unit vectors cos .THETA. and sin .THETA. are obtained from a phase-locked loop 54 which is illustrated in FIG. 6. The phase-locked loop 54 obtains an instantaneous vector sum of the three-phase input voltages (V.sub.ia, V.sub.ib, V.sub.ic) by using a 3-to-2 phase transformer 50B that generates signals v.sub.di and v.sub.qi. These signals are conveyed to a phase detector 56. The phase detector output may be defined as: EQU sin (phase error)=vdi * cos .THETA.-vqi * sin .THETA.
In the equation, sin .THETA. and cos .THETA. are the values presently pointed to in a look-up table 58.
The phase detector 56 output is processed by a proportional plus integral (PI) controller 60 which provides fast response and zero steady-state tracking error. The PI controller 60 output is used to determine the count parameter of a timer or digital oscillator 62. The timer count value is decremented from the count parameter value at a constant rate, when zero is reached the sin .THETA. and cos .THETA. pointers in the look-up table 58 are incremented. Since this is a closed-loop system, the timer count value is either increased or decreased, depending on the PI controller 60 output, so as to reduce the phase error until a phase-locked condition is achieved. Naturally, a hardware implementation of the phase-locked loop may also be used.
Returning to FIG. 5, in the synchronously rotating de-qe reference frame at synchronous frequency .THETA., the components of signals I.sup.e.sub.sqs and I.sup.e.sub.sds at the fundamental frequency .THETA., are transformed to dc quantities and all the harmonics are transformed to non-dc quantities and undergo a frequency shift in the spectrum. Low-pass filters 70 are used to yield dc signals, I.sup.e.sub.sqsdc and I.sup.e.sub.sdsdc, in the synchronous reference frame. The dc signals correspond to the fundamental component of the source current. A rotating-to-stationary transformer 72A is used to transform the signals from the synchronous reference frame to a stationary reference frame. In particular, the rotating-to-stationary transformer 72A executes the following equation: ##EQU4##
The stationary reference frame output signals I.sup.s.sub.sqsf and I.sup.s.sub.sdsf, are transformed to a three-phase signal with a 2-to-3 phase transformer 74A that executes the following equation: ##EQU5##
The 2-to-3 phase transformer 74A yields three-phase reference source currents i.sup.*.sub.sa, i.sup.*.sub.sb, and i.sup.*.sub.sc. The reference currents are then applied to the series filter 34 by means of an appropriate modulator as known by those skilled in the art. The series active filter is in series with the supply, the current reference signals are derived from the supply currents.
Since any non-dc components in the synchronous reference frame are attributed to harmonics in the three-phase reference frame, low-pass filtering of the synchronous reference frame signal yields the fundamental source current in the three-phase reference frame.
While this approach seems highly desirable, there are still a number of problems associated with it. First, the passive filter provides additional fundamental reactive power which can be highly undesirable for high displacement factor loads, such as Adjustable Speed Drives (ASDs) with diode or thyristor input side converters and cycloconverters. Next, this may result in a leading power factor. Another problem is that there is a potential for instability for some loads, such as, ASDs with diode or thyristor input side converters with high pass input filter capacitors. Another problem is that it is not a cost effective solution as it increases the cost of the overall passive filter system. In lower-power, cost-sensitive applications, it is important to keep the design of the passive filter as simple as possible. Tuned LC passive filters are custom components that can be expensive. Tuned LC passive filters must be sharply tuned to obtain characteristics similar to a notch filter. This requirement results in large passive filter rating and size.
Another problem with passive filters relates to distortion. As the line current is sinusoidal, all harmonic currents are forced into the passive filter, causing possibly unacceptable voltage distortion components at those frequencies where the passive filter does not have a very low impedance. Further, the passive filter has to be designed to handle the entire harmonic content of the non-linear load. This increases the kVA rating of the passive filter.
Another problem associated with the system of FIG. 1 is that the higher harmonic (&gt;=11th) load currents may result in appreciable voltage Total Harmonic Distortion (THD) at the passive filter terminals, due to the finite impedance of the shunt passive filter system at higher harmonic frequencies. That is, voltage distortion at the passive filter is equivalent to the product of the impedance at a given frequency and the existing harmonic currents. Since the passive filter is largely directed to absorbing 5th and 7th harmonics, appreciable impedance exists for higher harmonics. As a result, the presence of any higher order harmonics at the passive filter produces significant voltage distortion.
In the presence of voltage distortion at the passive filter, the load is supplied by a non-sinusoidal voltage. Due to the nonlinear nature of the load, the non-sinusoidal voltage may result in an increase or decrease of the original load harmonic current amplitudes and may also result in generation of new load harmonics. Further, the non-sinusoidal terminal voltage may be highly objectionable for voltage harmonic sensitive loads. In view of these problems, it would be highly desirable to provide a technique for reducing passive filter terminal voltage distortion.